论文标题
在分子和半限定板之间的范德华相互作用上
On the van der Waals interaction between a molecule and a half-infinite plate
论文作者
论文摘要
我们考虑在邻苯二甲胺的近似中与无限厚度相互作用的分子，即半空间，它是完美的导电或介电。在物理文献中已经知道，在这种情况下，原子或分子在足够大的距离上被板吸引。这种作用类似于中性原子或分子之间已知的范德华的相互作用。我们证明，系统的相互作用能量$ w $由$ W（r，v）= -c（v）r^{ - 3} + \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {o}（r^{ - 4}）$，其中$ r $是分子和板和$ v $之间的距离，表示其相对方向。此外，$ c（v）$是正且连续的，因此，对于所有相对取向$ v $，原子或分子总是在足够大的距离上朝板拉动。对于某些特定系统，我们提供$ W（r，v）$的清晰估计。这种渐近行为是很好的 - 但是，在物理文献中，即使在系统的基态存在下，我们也不知道以前的任何严格结果。出于教学原因，我们经常从氢原子的情况开始，然后将论点推广到处理通用分子。
We consider a molecule in the Born-Oppenheimer approximation interacting with a plate of infinite thickness, i.e, a half--space, which is perfectly conducting or dielectric. It is well--known in the physics literature that in this case the atom or molecule is attracted by the plate at sufficiently large distances. This effect is analogous to the well--known van der Waals interaction between neutral atoms or molecules. We prove that the interaction energy $W$ of the system is given by $W(r,v)= -C(v)r^{-3} + \mathcal{O}(r^{-4})$, where $r$ is the distance between the molecule and the plate and $v$ indicates their relative orientation. Moreover, $C(v)$ is positive and continuous, thus the atom or molecule is always pulled towards the plate at sufficiently large distances, for all relative orientations $v$. For some specific systems we provide sharper estimates of $W(r,v)$. This asymptotic behavior is well--known in the physics literature, however, we are not aware of any previous rigorous results, even on existence of a ground state of the system. For pedagogical reasons, we often start with the case of a hydrogen atom and then we generalize the arguments to deal with a general molecule.
